The 32-year-old Namibia international departed Swindon by mutual consent earlier on Monday, with six months remaining on his deal at the County Ground.
Risser signed for the Robins in 2001 and made 40 appearances last term, scoring four goals, as the Wiltshire club clinched the League Two title, with one of those coming at the EBB Stadium against brother Wilko when he lined up for the Shots.
However, Risser was deemed surplus to requirements by Town this term and spent the first half of the campaign on loan at Stevenage.
Aldershot boss Dean Holdsworth said: "I am delighted with the signing of Oliver. He is a strong, adaptable player who will fit in well with the squad.
"He also played a valuable part in Swindon Town's championship-winning side last season and will provide excellent experience for us. This is a good acquisition and I am delighted with this news."
Meanwhile, the Shots' rearranged fixtures against Northampton and Torquay have been set for Tuesday January 22 and Tuesday February 19 respectively.